Light a charcoal grill, and when the coals are covered with white ash, push them to one side. Alternatively, preheat only one zone of a gas grill. Carefully lift the grate and set a foil drip pan in the unheated zone; replace the grate. Stuff the chicken cavity with the lemon halves and thyme sprigs and season the chicken all over with salt and pepper.
If you are using a charcoal grill, thoroughly soak the wood chips, then drain. For a gas grill, wrap the chips in a foil packet and puncture the foil all over. Add the chips to the fire or gas flames and heat until they begin to smoke. Set the chicken on the grate over the drip pan. Cover the grill and smoke the chicken over low heat until golden and an instant-read thermometer inserted into the thigh registers 165°, about 1 hour 15 minutes. Let the chicken rest for 10 minutes before carving, then serve.
The grill-smoked chicken can be refrigerated for up to 3 days.